The general type of finite-part singular integrals and integral equations with logarithmic singularities used in fracture mechanics

1988 ◽  
Vol 75 (1-4) ◽  
pp. 275-285 ◽  
Author(s):  
E. G. Ladopoulos
Keyword(s):  
Fracture Mechanics ◽  
Integral Equations ◽  
General Type ◽  
Singular Integrals ◽  
Finite Part ◽  
Logarithmic Singularities

scholarly journals Integral equations with hypersingular kernels––theory and applications to fracture mechanics

2003 ◽  
Vol 41 (7) ◽  
pp. 683-720 ◽  
Author(s):  
Youn-Sha Chan ◽  
Albert C. Fannjiang ◽  
Glaucio H. Paulino
Keyword(s):  
Fracture Mechanics ◽  
Integral Equations

scholarly journals Approximation to Logarithmic-Cauchy Type Singular Integrals with Highly Oscillatory Kernels

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 728 ◽  
Author(s):  
SAIRA ◽  
Shuhuang Xiang
Keyword(s):  
Singular Integrals ◽  
Oscillatory Integral ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Cauchy Kernel ◽  
Cauchy Type ◽  
Highly Oscillatory ◽  
Logarithmic Singularities ◽  
Highly Oscillatory Integrals ◽  
Modified Moments

In this paper, a fast and accurate numerical Clenshaw-Curtis quadrature is proposed for the approximation of highly oscillatory integrals with Cauchy and logarithmic singularities, ⨍ − 1 1 f ( x ) log ( x − α ) e i k x x − t d x , t ∉ ( − 1 , 1 ) , α ∈ [ − 1 , 1 ] for a smooth function f ( x ) . This method consists of evaluation of the modified moments by stable recurrence relation and Cauchy kernel is solved by steepest descent method that transforms the oscillatory integral into the sum of line integrals. Later theoretical analysis and high accuracy of the method is illustrated by some examples.

Thermoelastic fracture mechanics with regularized hypersingular boundary integral equations

1999 ◽  
Vol 23 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Yu Xie Mukherjee ◽  
Ketan Shah ◽  
Subrata Mukherjee
Keyword(s):  
Fracture Mechanics ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral
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